Hochschild Cohomology of the Algebra of Conformal Endomorphisms

Hochschild Cohomology of the Algebra of Conformal Endomorphisms Full article

Journal

Известия Иркутского государственного университета. Серия: Математика (Bulletin of Irkutsk State University. Series Mathematics)
ISSN: 1997-7670

Output data

Year: 2026, Volume: 56, Pages: 129-144 Pages count : 16 DOI: 10.26516/1997-7670.2026.56.129

Tags

conformal algebra, Hochschild cohomology, Groebner–Shirshov basis, Morse matching

Authors

Kolesnikov P.S. ¹ , Alhussein H. ^2,3,4

Affiliations

1	Sobolev Institute of Mathematics SB RAS
2	Siberian State University of Telecommunication and Informatics
3	Novosibirsk State University of Economics and Management, Novosibirsk, Russian Federation
4	Novosibirsk State University, Novosibirsk, Russian Federation

Funding (1)

Министерство науки и высшего образования РФ

FWNF-2026-0017

It was proved by I. Dolguntseva (St. Peterburg Math. J., 2010) that second Hochschild cohomology groups for the associative conformal algebra with coefficients in an arbitrary conformal bimodule are trivial. In this work, we prove the same for all higher Hochschild cohomologies of by means of algebraic discrete Morse theory applied to the bar complex of the 1st Weyl algebra.

Kolesnikov P.S. , Alhussein H.
Hochschild Cohomology of the Algebra of Conformal Endomorphisms
Известия Иркутского государственного университета. Серия: Математика (Bulletin of Irkutsk State University. Series Mathematics). 2026. Т.56. С.129-144. DOI: 10.26516/1997-7670.2026.56.129 Scopus OpenAlex

Submitted:	Oct 21, 2025
Accepted:	Jan 19, 2026
Published online:	Jun 15, 2026

≡ Scopus:	2-s2.0-105041296385
≡ OpenAlex:	W7163994218